Add enum property to existing dropdown menu
scene.cycles.bake_type is already registered as a property of the CyclesRenderSettings class.  We can get the details of the enum from the class itself, or in the example below from  the instance; scene.cycles.rna_type.properties("bake_type")

Add a new item to the enum property list and redefine the property with our appended list.  



import bpy
from bpy.props import EnumProperty

context = bpy.context
scene = context.scene
prop = scene.cycles.rna_type.properties["bake_type"]
items = [(i.identifier, i.name, i.description, i.icon, i.value) 
              for i in prop.enum_items.values()]

# add one
if 'FOO' not in [i[0] for i in items]:
    items.append(('FOO', "Foo", "New Foo Item", 'NONE', 11))

    bpy.types.CyclesRenderSettings.bake_type = EnumProperty(
                                             name=prop.name,
                                             description=prop.description,
                                             default=prop.default,
                                             items=items)


Would need to append a draw method to the panel that recognises the new enum prop 'FOO'. 

Note: could get some hassles if cycles code doesn't know what to do with your new bake_type.